Blender How can I extrude a cylinder outward
This is a great case for spin modeling. There are two way to do this, you can use the screw modifier (I prefer this way); or you can use the spin tool in edit mode.
I will just describe the process to use the modifier, the modeling it exactly the same for either method; however using the spin tool is destructive (and a little harder to set up).

Start by creating the outline of the shape. This could be done using curves or a mesh object. I used a mesh object, and just extruded a few vertices to make half the shape. Take note of where the object origin is, the origin (highlighted in red) is where the modifier, by default, spins around.


All that is left to do is add the modifier. The default values work very well, provided you modeled the object around the Z axis. The only setting you need to be sure to turn on is Calc Order. That setting makes the normals consistent (sometimes you will then need to then check Flip because they will be backwards).